# 151-0213-00L  Fluid Dynamics with the Lattice Boltzmann Method

 Semester Autumn Semester 2020 Lecturers I. Karlin Periodicity yearly recurring course Language of instruction English

 Abstract The course provides an introduction to theoretical foundations and practical usage of the Lattice Boltzmann Method for fluid dynamics simulations. Objective Methods like molecular dynamics, DSMC, lattice Boltzmann etc are being increasingly used by engineers all over and these methods require knowledge of kinetic theory and statistical mechanics which are traditionally not taught at engineering departments. The goal of this course is to give an introduction to ideas of kinetic theory and non-equilibrium thermodynamics with a focus on developing simulation algorithms and their realizations.During the course, students will be able to develop a lattice Boltzmann code on their own. Practical issues about implementation and performance on parallel machines will be demonstrated hands on. Central element of the course is the completion of a lattice Boltzmann code (using the framework specifically designed for this course). The course will also include a review of topics of current interest in various fields of fluid dynamics, such as multiphase flows, reactive flows, microflows among others.Optionally, we offer an opportunity to complete a project of student's choice as an alternative to the oral exam. Samples of projects completed by previous students will be made available. Content The course builds upon three parts: I Elementary kinetic theory and lattice Boltzmann simulations introduced on simple examples. II Theoretical basis of statistical mechanics and kinetic equations.III Lattice Boltzmann method for real-world applications.The content of the course includes:1. Background: Elements of statistical mechanics and kinetic theory: Particle's distribution function, Liouville equation, entropy, ensembles; Kinetic theory: Boltzmann equation for rarefied gas, H-theorem, hydrodynamic limit and derivation of Navier-Stokes equations, Chapman-Enskog method, Grad method, boundary conditions; mean-field interactions, Vlasov equation; Kinetic models: BGK model, generalized BGK model for mixtures, chemical reactions and other fluids.2. Basics of the Lattice Boltzmann Method and Simulations:Minimal kinetic models: lattice Boltzmann method for single-component fluid, discretization of velocity space, time-space discretization, boundary conditions, forcing, thermal models, mixtures.3. Hands on: Development of the basic lattice Boltzmann code and its validation on standard benchmarks (Taylor-Green vortex, lid-driven cavity flow etc).4. Practical issues of LBM for fluid dynamics simulations:Lattice Boltzmann simulations of turbulent flows; numerical stability and accuracy.5. Microflow:Rarefaction effects in moderately dilute gases; Boundary conditions, exact solutions to Couette and Poiseuille flows; micro-channel simulations.6. Advanced lattice Boltzmann methods:Entropic lattice Boltzmann scheme, subgrid simulations at high Reynolds numbers; Boundary conditions for complex geometries.7. Introduction to LB models beyond hydrodynamics:Relativistic fluid dynamics; flows with phase transitions. Lecture notes Lecture notes on the theoretical parts of the course will be made available.Selected original and review papers are provided for some of the lectures on advanced topics. Handouts and basic code framework for implementation of the lattice Boltzmann models will be provided. Prerequisites / Notice The course addresses mainly graduate students (MSc/Ph D) but BSc students can also attend.